Triangle Similarity Calculator

Test if two triangles are similar using AA, SSS ratio, or SAS ratio criteria with detailed verification.

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If two angles of one triangle equal two angles of another, the triangles are similar.

Triangle 1
Triangle 2

Result

Similarity Test
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Step-by-Step Verification

Understanding Triangle Similarity

Two triangles are similar if they have the same shape but not necessarily the same size. Similar triangles have equal corresponding angles and proportional corresponding sides. The ratio between corresponding sides is called the scale factor.

Similarity Criteria

AA (Angle-Angle)

If two angles of one triangle are congruent to two angles of another, the triangles are similar. The third angles must also be equal since all angles sum to 180 degrees.

If angle A1 = angle A2 and angle B1 = angle B2, then similar

SSS (Side-Side-Side) Ratio

If all three pairs of corresponding sides are proportional (have the same ratio), the triangles are similar.

a1/a2 = b1/b2 = c1/c2 = k

SAS (Side-Angle-Side) Ratio

If two pairs of corresponding sides are proportional and the included angles are equal, the triangles are similar.

a1/a2 = b1/b2 and angle1 = angle2

Scale Factor

The scale factor (k) is the ratio of corresponding sides between similar triangles. If Triangle 2 is a scaled version of Triangle 1 with scale factor k, then every side of Triangle 2 is k times the corresponding side of Triangle 1. Areas scale by k² and perimeters scale by k.

Properties of Similar Triangles

  • Corresponding angles are equal.
  • Corresponding sides are in the same ratio (scale factor).
  • The ratio of perimeters equals the scale factor k.
  • The ratio of areas equals k² (scale factor squared).
  • Similarity is reflexive, symmetric, and transitive.
  • All equilateral triangles are similar to each other.